We created an efficient algorithm suitable for graphics processing units (GPUs) to perform Monte Carlo simulations of a subset of reaction-diffusion models. The algorithm uses techniques that are specific to GPU programming, and combines these with the multispin technique known from CPU programming to create one of the fastest algorithms for reaction-diffusion models. As an example, the algorithm is applied to the pair contact process with diffusion (PCPD). Compared to a simple algorithm on the CPU, our GPU algorithm is approximately 4000 times faster. If we compare the performance of the GPU algorithm, between the GPU and CPU, we find a speed-up of about 130x.